Optimal control of multistage deterministic, stochastic and fuzzy processes in the fuzzy environment via an evolutionary algorithm

This paper deals with the problem of control of deterministic, stochastic and fuzzy systems with a fixed termination time and fuzzy constraints imposed on controls and states. Constrains imposed on the system are given as membership functions of particular fuzzy sets. Transition functions for controlled systems are given as a matrix of transitions between states for a deterministic object, a matrix of probabilities of transitions for a stochastic object and a matrix of membership functions of transitions for a fuzzy system. An optimal (or sub-optimal) control is obtained using a specialized evolutionary algorithm (EA), which is a development over the previously used methods based on simple genetic algorithm. The specialized EA seems to be a very effective tool for solving such a class of optimization problems, comparing advantageously with the traditional simple genetic algorithm approach and with the previously used solutions like dynamic programming or branch and bound. The specialization of the applied EA is obtained using dedicated problem encoding, the method of ranking of genetic operators and the controlled selection of population members.